Assume That Your Population Regression Function Is $Y _ { i } = \beta _ { 1 } X _ { i } + u _ { i }$

Essay

Assume that your population regression function is $Y _ { i } = \beta _ { 1 } X _ { i } + u _ { i }$ i.e., a regression through the origin (no intercept).Under the homoskedastic
normal regression assumptions, the t-statistic will have a Student t distribution
with n-1 degrees of freedom, not n-2 degrees of freedom, as was the case in
Chapter 5 of your textbook.Explain.Do you think that the residuals will still sum
to zero for this case?